The simplification of Equations for Variable

Variable-Radius Circles in Constructive Geometric Constraint Solving
Ching-Shoei Chiang
Computer and Information Science
Soochow University
[email protected]
Variable-radius circles are common constructs in planar constraint solving and are
usually not handled fully by algebraic constraint solvers. We give a complete
treatment of variable-radius circles when such a circle must be determined
simultaneously with placing two groups of geometric entities. The problem arises for
instance in solvers using triangle decomposition to reduce the complexity of the
constraint problem.
The constraint on the variable-radius circle is the distance to its circumference or its
center, and the relative motions on the considered clusters are translational and
rotational. This talk covers the summary of three papers. Two papers, cooperated with
Professor Christoph Hoffmann, treat the circumference constraints, and the other one,
cooperated with Professor Robert Joan-Arinyo, treats the center constraints in
geometric constraint solving.